Question

I need help understand how to do this problem. Use the formula for computing future value using compound interest to determine the value of an account at the end of 10 years if a principal amount of $4,000 is deposited in an account at an annual interest rate of 4% and the interest is compounded monthly.

Answer 1

The amount after 10 years will be $5963.33

Step-by-step explanation:

The formula for compound interest is:

`A=P(1+(r)/(n))^(nt)`

Where:

P is the initial amount deposited

r is the rate of compounding, in decimal

n is the number of times interest is compounded for every unit of t

t is the time

In this case:

P = $4000

r is given in percentage. We need to divide by 100 in order to convert it to decimal:

`r=(4)/(100)=0.04`

Since this is compounded monthly, is compounded twelve times every year. Thus n = 12

And we want to know the amount after 10 years, thus t = 10

We can write now:

`A=4000(1+(0.04)/(12))^(12\cdot10)`

We can solve:

`A=4000\cdot(301)/(300)^(120)=5963.33073`

To the nearest cent, A = $5963.33